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EN
We consider an optimal control problem for a general mathematical model of drug treatment with a single agent. The control represents the concentration of the agent and its effect (pharmacodynamics) is modelled by a Hill function (i.e., Michaelis-Menten type kinetics). The aim is to minimize a cost functional consisting of a weighted average related to the state of the system (both at the end and during a fixed therapy horizon) and to the total amount of drugs given. The latter is an indirect measure for the side effects of treatment. It is shown that optimal controls are continuous functions of time that change between full or no dose segments with connecting pieces that take values in the interior of the control set. Sufficient conditions for the strong local optimality of an extremal controlled trajectory in terms of the existence of a solution to a piecewise defined Riccati differential equation are given.
EN
Cathodoluminescence (CL) technique is applied for evaluation of in-depth and in-plane variations of light emission from semiconductor heterostructures, including laser diode structures. Light emission properties of heteroepitaxial and heteroepitaxial structures, are studied. We demonstrate possibility of in-depth profiling of complicated multi quantum well structures, which allows us to evaluate light emission characteristics from different regions of, e.g., laser structures. Due to this property of the CL, we can evaluate interconnections between structural quality of the samples and light emission characteristics. Stimulated emission under electron bean pumping is achieved in a conventional CL, set up for selected heterostructures. Thereshold currents for stimulated emission are evaluated from the CL investigations. We demonstrate that potential fluctuations are not fully screened in the active regions of laser structures, even at large excitation densities.
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